{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Think Bayes solutions: Chapter 4\n",
    "\n",
    "This notebook presents solutions to exercises in Think Bayes.\n",
    "\n",
    "Copyright 2016 Allen B. Downey\n",
    "\n",
    "MIT License: https://opensource.org/licenses/MIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "\n",
    "import numpy as np\n",
    "\n",
    "import thinkbayes2\n",
    "from thinkbayes2 import Pmf, Cdf, Suite\n",
    "import thinkplot\n",
    "\n",
    "% matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Euro problem\n",
    "\n",
    "Here's a class that represents hypotheses about the probability a coin lands heads."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class Euro(Suite):\n",
    "\n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\"Computes the likelihood of `data` given `hypo`.\n",
    "        \n",
    "        data: string 'H' or 'T'\n",
    "        hypo: probability of heads, 0-100\n",
    "        \n",
    "        returns: float\n",
    "        \"\"\"\n",
    "        x = hypo\n",
    "        if data == 'H':\n",
    "            return x/100\n",
    "        else:\n",
    "            return 1 - x/100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can make a uniform prior and update it with 140 heads and 110 tails:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "suite = Euro(range(0, 101))\n",
    "dataset = 'H' * 140 + 'T' * 110\n",
    "\n",
    "for data in dataset:\n",
    "    suite.Update(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's what the posterior looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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B1T9RrJRbAlYPDgGzCiWXkXZLwBYqh4BZhZITxTwmYAuVQ8CsQrV6oMykbj9i0urAIWBW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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe71d597d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Pdf(suite)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can summarize the posterior several ways, including the mean:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "55.952380952380956"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "suite.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Median:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "56"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "suite.Percentile(50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The peak of the posterior, known as the Maximum Aposteori Probability (MAP)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "56"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "suite.MAP()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And a 90% credible interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(51, 61)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "suite.CredibleInterval(90)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can look up a particular value in the posterior PMF, but the result doesn't mean much, because we could have divided the range (0-100) into as many pieces as we like, and the result would be different."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.02097652612954468"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "suite.Prob(50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Different priors\n",
    "\n",
    "Let's see how that looks with different priors.\n",
    "\n",
    "Here's a function that makes a uniform prior:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def UniformPrior(label='uniform'):\n",
    "    \"\"\"Makes a Suite with a uniform prior.\"\"\"\n",
    "    suite = Euro(range(0, 101), label=label)\n",
    "    return suite"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And another that makes a triangular prior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def TrianglePrior(label='triangle'):\n",
    "    \"\"\"Makes a Suite with a triangle prior.\"\"\"\n",
    "    suite = Euro(label=label)\n",
    "    for x in range(0, 51):\n",
    "        suite[x] = x\n",
    "    for x in range(51, 101):\n",
    "        suite[x] = 100-x \n",
    "    suite.Normalize()\n",
    "    return suite"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what they look like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/J2CNuxe4+14CY44NLNVmIDAbwN3fARqaWU5wejmwNcx6BwJ/Db7/K/DzKvRN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\ngfmaAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe6ec6df490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "triangle = TrianglePrior()\n",
    "uniform = UniformPrior()\n",
    "suites = [triangle, uniform]\n",
    "\n",
    "thinkplot.Pdfs(suites)\n",
    "thinkplot.Config(xlabel='x', ylabel='Probability')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we update them both with the same data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def RunUpdate(suite, heads=140, tails=110):\n",
    "    \"\"\"Updates the Suite with the given number of heads and tails.\n",
    "\n",
    "    suite: Suite object\n",
    "    heads: int\n",
    "    tails: int\n",
    "    \"\"\"\n",
    "    dataset = 'H' * heads + 'T' * tails\n",
    "    for data in dataset:\n",
    "        suite.Update(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "for suite in suites:\n",
    "    RunUpdate(suite)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results are almost identical; the remaining difference is unlikely to matter in practice."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SZ1MAefnll4vdBJkh3cISKRFtnb2jU3hjMRYdpYRJtubGmkxZ95GROG29msorhaUAIlIi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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe6ec37f090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Pdfs(suites)\n",
    "thinkplot.Config(xlabel='x', ylabel='Probability')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The binomial likelihood function\n",
    "\n",
    "We can make the Euro class more efficient by computing the likelihood of the entire dataset at once, rather than one coin toss at a time.\n",
    "\n",
    "If the probability of heads is p, we can compute the probability of k=140 heads in n=250 tosses using the binomial PMF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Euro2(thinkbayes2.Suite):\n",
    "    \"\"\"Represents hypotheses about the probability of heads.\"\"\"\n",
    "\n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\"Computes the likelihood of the data under the hypothesis.\n",
    "\n",
    "        hypo: integer value of x, the probability of heads (0-100)\n",
    "        data: tuple of (number of heads, number of tails)\n",
    "        \"\"\"\n",
    "        x = hypo / 100.0\n",
    "        heads, tails = data\n",
    "        like = x**heads * (1-x)**tails\n",
    "        return like"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I left out the binomial coefficient ${n}\\choose{k}$ because it does not depend on `p`, so it's the same for all hypotheses.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.6088321798736822e-76"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "suite = Euro2(xrange(0, 101))\n",
    "dataset = 140, 110\n",
    "suite.Update(dataset)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what the posterior looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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B1T9RrJRbAlYPDgGzCiWXkXZLwBYqh4BZhZITxTwmYAuVQ8CsQrV6oMykbj9i0urAIWBW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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe6ec254f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Pdf(suite)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Beta distribution\n",
    "\n",
    "The Beta distribution is a conjugate prior for the binomial likelihood function, which means that if you start with a Beta distribution and update with a binomial likelihood, the posterior is also Beta.\n",
    "\n",
    "Also, given the parameters of the prior and the data, we can compute the parameters of the posterior directly.  The following class represents a Beta distribution and provides a constant-time Update method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy import special\n",
    "\n",
    "class Beta:\n",
    "    \"\"\"Represents a Beta distribution.\n",
    "\n",
    "    See http://en.wikipedia.org/wiki/Beta_distribution\n",
    "    \"\"\"\n",
    "    def __init__(self, alpha=1, beta=1, label=None):\n",
    "        \"\"\"Initializes a Beta distribution.\"\"\"\n",
    "        self.alpha = alpha\n",
    "        self.beta = beta\n",
    "        self.label = label if label is not None else '_nolegend_'\n",
    "\n",
    "    def Update(self, data):\n",
    "        \"\"\"Updates a Beta distribution.\n",
    "\n",
    "        data: pair of int (heads, tails)\n",
    "        \"\"\"\n",
    "        heads, tails = data\n",
    "        self.alpha += heads\n",
    "        self.beta += tails\n",
    "\n",
    "    def Mean(self):\n",
    "        \"\"\"Computes the mean of this distribution.\"\"\"\n",
    "        return self.alpha / (self.alpha + self.beta)\n",
    "\n",
    "    def MAP(self):\n",
    "        \"\"\"Computes the value with maximum a posteori probability.\"\"\"\n",
    "        a = self.alpha - 1\n",
    "        b = self.beta - 1\n",
    "        return a / (a + b)\n",
    "\n",
    "    def Random(self):\n",
    "        \"\"\"Generates a random variate from this distribution.\"\"\"\n",
    "        return random.betavariate(self.alpha, self.beta)\n",
    "\n",
    "    def Sample(self, n):\n",
    "        \"\"\"Generates a random sample from this distribution.\n",
    "\n",
    "        n: int sample size\n",
    "        \"\"\"\n",
    "        size = n,\n",
    "        return np.random.beta(self.alpha, self.beta, size)\n",
    "\n",
    "    def EvalPdf(self, x):\n",
    "        \"\"\"Evaluates the PDF at x.\"\"\"\n",
    "        return x ** (self.alpha - 1) * (1 - x) ** (self.beta - 1)\n",
    "\n",
    "    def MakePmf(self, steps=101, label=None):\n",
    "        \"\"\"Returns a Pmf of this distribution.\n",
    "\n",
    "        Note: Normally, we just evaluate the PDF at a sequence\n",
    "        of points and treat the probability density as a probability\n",
    "        mass.\n",
    "\n",
    "        But if alpha or beta is less than one, we have to be\n",
    "        more careful because the PDF goes to infinity at x=0\n",
    "        and x=1.  In that case we evaluate the CDF and compute\n",
    "        differences.\n",
    "\n",
    "        The result is a little funny, because the values at 0 and 1\n",
    "        are not symmetric.  Nevertheless, it is a reasonable discrete\n",
    "        model of the continuous distribution, and behaves well as\n",
    "        the number of values increases.\n",
    "        \"\"\"\n",
    "        if label is None and self.label is not None:\n",
    "            label = self.label\n",
    "\n",
    "        if self.alpha < 1 or self.beta < 1:\n",
    "            cdf = self.MakeCdf()\n",
    "            pmf = cdf.MakePmf()\n",
    "            return pmf\n",
    "\n",
    "        xs = [i / (steps - 1) for i in range(steps)]\n",
    "        probs = [self.EvalPdf(x) for x in xs]\n",
    "        pmf = Pmf(dict(zip(xs, probs)), label=label)\n",
    "        return pmf\n",
    "\n",
    "    def MakeCdf(self, steps=101):\n",
    "        \"\"\"Returns the CDF of this distribution.\"\"\"\n",
    "        xs = [i / (steps - 1) for i in range(steps)]\n",
    "        ps = special.betainc(self.alpha, self.beta, xs)\n",
    "        cdf = Cdf(xs, ps)\n",
    "        return cdf\n",
    "\n",
    "    def Percentile(self, ps):\n",
    "        \"\"\"Returns the given percentiles from this distribution.\n",
    "\n",
    "        ps: scalar, array, or list of [0-100]\n",
    "        \"\"\"\n",
    "        ps = np.asarray(ps) / 100\n",
    "        xs = special.betaincinv(self.alpha, self.beta, ps)\n",
    "        return xs\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's how we use it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5595238095238095"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta = Beta()\n",
    "beta.Update((140, 110))\n",
    "beta.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's the posterior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Kf5EKhcs5q+Uv843CX6RC4QQv9fnLfKPwF6lQUg9yyenSoxwlQQp/kQoNJDjJCwrvI+iB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\nfKftg/U8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe6ec188210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Pdf(beta.MakePmf())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Amazing, no?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** One way to construct priors is to make a Beta distribution and adjust the parameters until it has the shape you want.  Then when you do an update, the data get added to the parameters of the prior.  Since the parameters of the prior play the same mathematical role as the data, they are sometimes called \"precounts\".\n",
    "\n",
    "Suppose you believe that most coins are fair or unlikely to deviate from 50% by more than a few percentage points.  Construct a prior that captures this belief and update it with the Euro data.  How much effect does it have on the posterior, compared to the uniform prior?\n",
    "\n",
    "Hint: A Beta distribution with parameters `(1, 1)` is uniform from 0 to 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe6ec0ce390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# Here's the uniform prior\n",
    "    \n",
    "uniform = Beta(1, 1, label='uniform')\n",
    "thinkplot.Pdf(uniform.MakePmf())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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l1+LaDWvY+a8+lH89MHyO//XQE9z15W+x74cHOPCb39E3ODqvVgHV30c8WiKU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\nfKftg/U8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe6ec08bf90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# And here's what it looks like after the update\n",
    "    \n",
    "uniform.Update(dataset)\n",
    "thinkplot.Pdf(beta.MakePmf())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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36N8/+nSI6qTfT17encj3wvFil8TYmOMOo2NjjI6NMTw8yvnhEQaHRjg7eJ4z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\nEZEMUviLiGSQwl9EJIMU/iIiGfT/AbA7dFKOVFcDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe6ebfb2a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# Here's a beta prior with precounts chosen to represent\n",
    "# out background knowledge about coins.\n",
    "    \n",
    "beta = Beta(100, 100, label='beta')\n",
    "thinkplot.Pdf(beta.MakePmf())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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d/4vhl3KsjS1WDn9bkp558Y3q9i0F6vKZ8U9/7n3V7b97fh8nT5/JsTa2GDn8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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe6ebef1190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# And here's what it looks like after the update\n",
    "    \n",
    "beta.Update(dataset)\n",
    "thinkplot.Pdf(beta.MakePmf())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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kcLwh/3pVmlUlk8n8g3rdunVTflbYFscFwMnuHgcwsx8AzwA5A4e7j5nZFcD9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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe6ebea3110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# Comparing the two, we see that the (more) informative\n",
    "# prior influences the location and spread of the\n",
    "# posterior.\n",
    "    \n",
    "thinkplot.Pdf(beta.MakePmf())\n",
    "thinkplot.Pdf(uniform.MakePmf())\n",
    "thinkplot.Config(xlabel='x', ylabel='Probability')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Exercise:**  At the 2016 Summer Olympics in the Women's Skeet event, Kim Rhode faced Wei Meng in the bronze medal match.  They each hit 15 of 25 skeets, sending the match into sudden death.  In the first round, both hit 1 of 2 skeets.  In the next two rounds, they each hit 2 skeets.  Finally, in the fourth round, Rhode hit 2 and Wei hit 1, so Rhode won the bronze medal, making her the first Summer Olympian to win an individual medal at six consecutive summer games.\n",
    "\n",
    "But after all that shooting, what is the probability that Rhode is actually a better shooter than Wei?  If the same match were held again, what is the probability that Rhode would win?\n",
    "\n",
    "As always, you will have to make some modeling decisions, but one approach is to estimate, for each shooter, the probability of hitting a skeet.  Then, to estimate the probability that Rhode is a better shooter, you can draw samples from the two posterior distributions and compare them.  To estimate the probability of winning a rematch, you could draw samples from the posterior distributions and simulate a round of 25 shots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "# Here's a Beta distribution that represents Rhode's probability\n",
    "# of hitting a skeet\n",
    "\n",
    "rhode = Beta(1, 1, label='Rhode')\n",
    "rhode.Update((22, 11))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "# And another Beta for Wei\n",
    "\n",
    "wei = Beta(1, 1, label='Wei')\n",
    "wei.Update((21, 12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lxsNOASglogIAXQAOQAo8Si8C+DqAp4loG4BhIUQPEaUCsAghRogoGsAnAfxE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\nMbYg/x9DVr6xKQ8dDwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe6ec02efd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# Here's what the posteriors look like\n",
    "\n",
    "thinkplot.Pdf(rhode.MakePmf())\n",
    "thinkplot.Pdf(wei.MakePmf())\n",
    "thinkplot.Config(xlabel='x', ylabel='Probability')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.58960000000000001"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# To estimate the probability of superiority, we can\n",
    "# draw samples from the posteriors and compare them\n",
    "\n",
    "rhode_sample = rhode.MakeCdf(10001).Sample(10000)\n",
    "wei_sample = wei.MakeCdf(10001).Sample(10000)\n",
    "np.mean(rhode_sample > wei_sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.41020000000000001"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# The probability that Rhode is a better shooter is about 59%\n",
    "\n",
    "np.mean(rhode_sample < wei_sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Xz7HlXe9Z079zLXl869uknn8bxSjTOzuB01V1pqouAo8Ae4b67AEeBqiqo8DVSTaPuO2G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\nZ/I5jgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe6ec23d390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# To simulate a rematch, we can draw `p` from the posterior\n",
    "# distribution and then sample from a binomial distribution\n",
    "# with parameters `p` and `n=25`.\n",
    "\n",
    "rhode_rematch = np.random.binomial(25, rhode_sample)\n",
    "thinkplot.Hist(Pmf(rhode_rematch))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.52090000000000003"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# The probability that Rhode wins a rematch (without going\n",
    "# to sudden death) is about 52%\n",
    "\n",
    "wei_rematch = np.random.binomial(25, wei_sample)\n",
    "np.mean(rhode_rematch > wei_rematch)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.39079999999999998"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# The probability that Wei wins the rematch is 39%\n",
    "\n",
    "np.mean(rhode_rematch < wei_rematch)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.088300000000000003"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# And the chance that the rematch also goes to sudden death is\n",
    "# about 9%\n",
    "\n",
    "# Assuming that sudden death is close to 50/50, the overall chance\n",
    "# that Rhode winds is about 56%\n",
    "\n",
    "np.mean(rhode_rematch == wei_rematch)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise** Suppose that instead of observing coin tosses directly, you measure the outcome using an instrument that is not always correct. Specifically, suppose there is a probability `y` that an actual heads is reported as tails, or actual tails reported as heads.\n",
    "\n",
    "Write a class that estimates the bias of a coin given a series of outcomes and the value of `y`.\n",
    "\n",
    "How does the spread of the posterior distribution depend on `y`?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "# Here's a class that models an unreliable coin\n",
    "\n",
    "class UnreliableCoin(Suite):\n",
    "    \n",
    "    def __init__(self, prior, y):\n",
    "        \"\"\"\n",
    "        prior: seq or map\n",
    "        y: probability of accurate measurement\n",
    "        \"\"\"\n",
    "        Suite.__init__(self, prior)\n",
    "        self.y = y\n",
    "    \n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\"\n",
    "        data: outcome of unreliable measurement, either 'H' or 'T'\n",
    "        hypo: probability of heads, 0-100\n",
    "        \"\"\"\n",
    "        x = hypo / 100\n",
    "        y = self.y\n",
    "        if data == 'H':\n",
    "            return x*y + (1-x)*(1-y)\n",
    "        else:\n",
    "            return x*(1-y) + (1-x)*y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe6ec387a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# Now let's initialize one with `y=0.9`:\n",
    "\n",
    "prior = range(0, 101)\n",
    "suite = UnreliableCoin(prior, y=0.9)\n",
    "thinkplot.Pdf(suite)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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py3Ut9JZC1XQiwsO4d2bFvEuLVu2w7mJSyt8EVHJwb1IaM6ibjZGoYDUqpQt9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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe6ec01da10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# And update with 3 heads and 7 tails.\n",
    "\n",
    "for outcome in 'HHHTTTTTTT':\n",
    "    suite.Update(outcome)\n",
    "    \n",
    "thinkplot.Pdf(suite)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "# Now let's try it out with different values of `y`:\n",
    "\n",
    "def compute_prior(y):\n",
    "    prior = range(0, 101)\n",
    "    suite = UnreliableCoin(prior, y=y)\n",
    "    for outcome in 'HHHTTTTTTT':\n",
    "        suite.Update(outcome)\n",
    "    \n",
    "    thinkplot.Pdf(suite, label='y=%g' % y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KWLBgAe+//z6LFi06Z+7777/Pn/70J9atW0dMTAwbN27k+uuv59ChQyQm9twMy2rNfqSU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\ncdBoNBpNF/4fyqktaxIPLnAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe6ebe64850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# The posterior distribution gets wider as the measurement gets less reliable.\n",
    "\n",
    "compute_prior(1)\n",
    "compute_prior(0.8)\n",
    "compute_prior(0.6)\n",
    "thinkplot.config(legend=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe6ec0bde90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# At `y=0.5`, the measurement provides no information, so the posterior equals the prior:\n",
    "\n",
    "compute_prior(0.5)\n",
    "thinkplot.config(legend=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BS8jA8Cgnztdx7JyOyrqOWW20Wg0F+Wns3JxN4bp0AgPsN/+v3pnLf718Bb3B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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe6ec22ea50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# As the coin gets less reliable (below `y=0.5`) the distribution gets narrower again.  \n",
    "# In fact, a measurement with `y=0` is just as good as one with `y=1`, \n",
    "# provided that we know what `y` is.\n",
    "\n",
    "compute_prior(0.4)\n",
    "compute_prior(0.2)\n",
    "compute_prior(0.0)\n",
    "thinkplot.config(legend=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise** This exercise is inspired by a question posted by a “redditor” named dominosci on Reddit’s statistics “subreddit” at http://reddit.com/r/statistics.\n",
    "\n",
    "Reddit is an online forum with many interest groups called subreddits. Users, called redditors, post links to online content and other web pages. Other redditors vote on the links, giving an “upvote” to high-quality links and a “downvote” to links that are bad or irrelevant.\n",
    "\n",
    "A problem, identified by dominosci, is that some redditors are more reliable than others, and Reddit does not take this into account.\n",
    "\n",
    "The challenge is to devise a system so that when a redditor casts a vote, the estimated quality of the link is updated in accordance with the reliability of the redditor, and the estimated reliability of the redditor is updated in accordance with the quality of the link.\n",
    "\n",
    "One approach is to model the quality of the link as the probability of garnering an upvote, and to model the reliability of the redditor as the probability of correctly giving an upvote to a high-quality item.\n",
    "\n",
    "Write class definitions for redditors and links and an update function that updates both objects whenever a redditor casts a vote."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "# Here's one possible model:\n",
    "\n",
    "#  Each article has a quality Q, which is the probability of \n",
    "#  eliciting an upvote from a completely reliab;e redditor. \n",
    "\n",
    "#  Each user has a reliability R, which is the probability of\n",
    "#  giving an upvote to an item with Q=1.\n",
    "\n",
    "#  The probability that a redditor with reliability R gives an\n",
    "#  upvote to an item with quality Q is `R*Q + (1-R) * (1-Q)`\n",
    "\n",
    "# Now when a redditor votes on a item, we simultaneously update our\n",
    "# belief about the redditor and the item.\n",
    "\n",
    "class Redditor(Suite):\n",
    "    \"\"\"Represents hypotheses about the trustworthiness of a redditor.\"\"\"\n",
    "\n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\"Computes the likelihood of the data under the hypothesis.\n",
    "\n",
    "        hypo: integer value of r, the prob of a correct vote (0-100)\n",
    "        data: (vote, q) pair, where vote is 'up' or 'down' and\n",
    "              q is the mean quality of the link\n",
    "        \"\"\"\n",
    "        r = hypo / 100.0\n",
    "        vote, q = data\n",
    "\n",
    "        if vote == 'up':\n",
    "            return r * q + (1-r) * (1-q)\n",
    "        elif vote == 'down':\n",
    "            return r * (1-q) + (1-r) * q\n",
    "        else:\n",
    "            return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "    \n",
    "class Item(Suite):\n",
    "    \"\"\"Represents hypotheses about the quality of an item.\"\"\"\n",
    "\n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\"Computes the likelihood of the data under the hypothesis.\n",
    "\n",
    "        hypo: integer value of x, the prob of garnering an upvote\n",
    "        data: (vote, t) pair, where vote is 'up' or 'down' and\n",
    "              t is the mean trustworthiness of the redditor\n",
    "        \"\"\"\n",
    "        x = hypo / 100.0\n",
    "        vote, r = data\n",
    "\n",
    "        if vote == 'up':\n",
    "            return x * r + (1-x) * (1-r)\n",
    "        elif vote == 'down':\n",
    "            return x * (1-r) + (1-x) * r\n",
    "        else:\n",
    "            return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6699999999999996"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PAuOA1Cu2WQhMAGaXlslZ51yWmZ283m3NrLFz7sc31o8GttzqTkiw3QeOMyk9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\nykFERK6ichARkauoHERE5Cr/H3ZiC8kk9PV9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe6ec1c1810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "    \n",
    "# Suppose we start with a redditor who has demonstrated some reliability.\n",
    "\n",
    "from thinkbayes2 import Beta\n",
    "\n",
    "redditor = Redditor(label='redditor')\n",
    "beta = Beta(2, 1)\n",
    "for val, prob in beta.MakePmf().Items():\n",
    "    redditor.Set(val*100, prob)\n",
    "    \n",
    "thinkplot.Pdf(redditor)\n",
    "mean_r = redditor.Mean() / 100.0\n",
    "mean_r"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5000000000000001"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe6ebd728d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "    \n",
    "# And a completely unknown item.\n",
    "\n",
    "item = Item(range(0, 101), label='item')\n",
    "\n",
    "thinkplot.Pdf(item)\n",
    "mean_q = item.Mean() / 100.0\n",
    "mean_q"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4999999999999999"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "    \n",
    "# We update the priors simultaneously, each using the mean value of the other.\n",
    "\n",
    "redditor.Update(('up', mean_q))\n",
    "item.Update(('up', mean_r))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "67.0 (22.0, 98.0)\n"
     ]
    },
    {
     "data": {
      "image/png": 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J/CgwBhh7xTYLgAnArGCZnHXOZZnZyevd1swaOud+emP9CGDLre6EhNpz4DiT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\nReUgIiJXUTmIiMhVVA4iInKV/w+UZxDJ13twnQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe6ebd11590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "    \n",
    "# And here are the results.  Since we knew nothing about the item,\n",
    "# the vote provides no information about the redditor:\n",
    "\n",
    "thinkplot.Pdf(redditor)\n",
    "print(redditor.Mean(), redditor.CredibleInterval(90))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "55.78 (7, 97)\n"
     ]
    },
    {
     "data": {
      "image/png": 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QoH5CiBmKSGVQcZA7KigoYvm32/lk5UYuXw2+EzFtWC+mjhtKm5ZNQspORCqb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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fe6ebd57e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "    \n",
    "# But since we think the redditor is reliable, the vote provides \n",
    "# some information about the item:\n",
    "\n",
    "thinkplot.Pdf(item)\n",
    "print(item.Mean(), item.CredibleInterval(90))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "    \n",
    "# After the upvote, the mean quality of the item increases to about 56%.\n",
    "\n",
    "# The model I used to compute likelihoods is not the only choice.\n",
    "# As an alternative, I could have used something like \n",
    "# item response theory (https://en.wikipedia.org/wiki/Item_response_theory),\n",
    "# which we'll see in Chapter 12."
   ]
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